Texture Segmentation using the Boundary Contour System

[Paul Kube]

   Date: Thu, 13 Apr 89 14:47:57 +0200
   From: Dario Ringach <dario%TECHUNIX.BITNET at VMA.CC.CMU.EDU>

   How can the Boundary Contour System segment textures with identical
   second-order statistics?  

If by "segment" you mean construct a Boundary Contour between the two
textured regions, it probably won't.

   I mean, first-order differences are easily
   discovered by the "contrast sensitive" cells at the first stage of the
   BCS (the OC filter), 

Yes.

   while the CC-loop can account for second-order
   (dipole) statistics; 

The CC loop can construct linkages between texture elements with
similar orientation, and so can, to some extent, "group" elements into
regions with similar second-order statistics.  However there is
nothing in the BC system that is sensitive to such differences in 2nd
order statistics as may exist between regions, so it won't mark a
boundary between them, so it won't segment them, except perhaps by
accident (e.g. if end cuts of elements at the boundary between regions
happen to line up in the right way).

   but how can the BCS segment textures, as the ones
   presented by Julez, which have even identical third-order statistics
   but are easily discriminable?  

Indeed, but it doesn't even have the resources to segment correctly in the
iso-first-order case.

   Is the BCS/FCS model consistent with
   Julez's Textons theory?  If so, in which way?

I think it's most useful to see Grossberg and Mingolla (Perception and
Psychophysics 1985) as proposing a mechanism to account for some of
the linking, subjective contour, and neon spreading phenomena that
seem to be involved in some texture stimuli used by Beck.  In my way
of carving things up, this is a contribution to the texture
*description* problem.  Julesz has (almost) always studiously avoided
these kinds of effects in his displays so it has (almost) nothing to
say about his work.  In any case, it has nothing to say about the
texture *discrimination* problem, which is exactly the problem of
computing boundaries between differently textured image regions, given
some representation which shows them to be different.

Let me add that when I discussed these issues with Mingolla about a
year ago, he was optimistic that the BC/FC system might segment
Julesz's stimuli, though it hadn't been tried.  I was and remain
pessimistic, though to my knowledge the experiments still haven't
been done.

	--Paul Kube
	kube at ucsd.edu